Abstract. The sum of random variables are of interest in
many areas of the sciences. In teletraffic analysis, the sum of
Hyperexponential distribution is used as a model for the holding time
distribution. Many authors examined this model and discussed its probability
density function. In this paper, we consider the sum of independent
Hyper-Erlang distributions. We showed that the probability density function
of this distribution is related to probability density function of the sum
of independent Erlang distributions- the Hypoexponential distribution. As a
consequence, we find an exact closed expressions for the probability density
function of both distribution, which are related to the Kummer confluent
hypergeometric function.